# Pascals triangle problem(discrete mathematics)

1. Oct 28, 2012

### stanleyman

1. The problem statement, all variables and given/known data
Determine which row of pascals triangle contains 3 consecutive entries that are in the ratio 1:2:3.

2. Relevant equations
(n, k ) = n!/k!(n-k)!

3. The attempt at a solution
(n,k):(n,k+1):(n,k+2)
1 : 2: : 3

What I did was cross multiply.

2 times (n,k) = 1 times (n,k+1) and 3 times (n,k+1) = 2 times (n,k+2)
2(n!/(k!(n-k)!) = n!/(k+1)!(n-k-1)! and 3(n!/(k+1)!(n-k-1)!) = 2(n!/(k+2)!(n-k-2)!

I know that i should solve for n in the first equation then substitute n in the second equation to get n and k. I'm stuck on the algebra part.

2. Oct 28, 2012

### Mentallic

Well, what are some of the rules of factorials?

n! = n*(n-1)*(n-2)*...*2*1

n! = n*(n-1)!

So if we have an equation such as

n! = 10*(n-1)!

then to solve this, we would use the rule n! = n*(n-1)! to obtain

n*(n-1)! = 10*(n-1)!

then you can divide through by (n-1)! and find n=10. See if you can apply this rule to solve your equation.

3. Oct 30, 2012

### stanleyman

thank you i got the answer.